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arXiv · 1709.08869

Special elements of the lattice of monoid varieties

S. V. Gusev
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Abstract

We completely classify all neutral or costandard elements in the lattice $\mathbb{MON}$ of all monoid varieties. Further, we prove that an arbitrary upper-modular element of $\mathbb{MON}$ except the variety of all monoids is either a completely regular or a commutative variety. Finally, we verify that all commutative varieties of monoids are codistributive elements of $\mathbb{MON}$. Thus, the problems of describing codistributive or upper-modular elements of $\mathbb{MON}$ are completely reduced to the completely regular case.

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S. V. Gusev. 2017-11-29. Special elements of the lattice of monoid varieties. https://doi.org/10.1007/s00012-018-0513-0

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